Unique resonant normal forms for area-preserving maps at an elliptic fixed point
Gelfreich, Vassili and Gelfreikh, Natalia. (2009) Unique resonant normal forms for area-preserving maps at an elliptic fixed point. Nonlinearity, Vol.22 (No.4). pp. 783-810. ISSN 0951-7715Full text not available from this repository.
Official URL: http://dx.doi.org/10.1088/0951-7715/22/4/006
We study possible simplifications of normal forms for area-preserving maps near a resonant elliptic fixed point. In the generic case we prove that at all orders the Takens normal form vector field can be transformed to the particularly simple form described by the formal interpolating Hamiltonian
H = I-2 A(I) + I-n/2 B(I) cos n phi.
The form of formal series A and B depends on the order of the resonance n. For each n >= 3 we establish which terms of the series can be eliminated by a canonical substitution and derive a unique normal form which provides a full set of formal invariants with respect to canonical changes in coordinates.
We extend these results to families of area-preserving maps. Then the formal interpolating Hamiltonian takes a form similar to the case of an individual map but involves formal power series in action I and the parameter.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Nonlinearity|
|Publisher:||Institute of Physics Publishing Ltd.|
|Official Date:||April 2009|
|Number of Pages:||28|
|Page Range:||pp. 783-810|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Royal Society (Great Britain)|
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